This invention relates generally to equipment and methods for testing electronic devices, and more particularly to a technique for extracting from an electronic test signal the amplitudes of the test signal""s frequency components.
Test programs for automatic test systems commonly require a tester to measure the power spectrum of a signal sampled from a device under test (DUT). In a conventional testing scenario, an automatic test system generates a stimulus for exercising an input of a DUT and samples the output of the DUT as the DUT responds to the stimulus. Tester software computes the power spectrum of the sampled output signal by performing a Discrete Fourier Transform (DFT) on the samples acquired.
As is known, an error called xe2x80x9cleakagexe2x80x9d manifests itself in power spectra produced by a DFT whenever the sample clock is not xe2x80x9ccoherentxe2x80x9d with the sampled signal. The sample clock is xe2x80x9ccoherentxe2x80x9d if its frequency is a precise integer multiple of each frequencies present in the signal being sampled. Leakage is the mathematical consequence of performing a DFT on truncated frequenciesxe2x80x94i.e., frequencies that do not complete a full cycle within the sample window. Leakage can be observed as an erroneous broadening of spectral lines, a creation of false peaks and troughs (lobes), and a general elevation of the power spectrum""s noise floor.
Several methods have been devised to reduce leakage. One method is to increase sampling rate. In general, the higher the sampling rate, the smaller the amount of truncation in the frequency range of interest and the smaller the leakage error. Although effective, increasing sampling rate reduces leakage only in proportion to the magnitude of the increase. It also tends to greatly increase the cost of the sampling equipment used.
Another common technique for reducing leakage is to multiply the sampled data sequence by a windowing function. The windowing function has the effect of tapering the sampled data sequence around its endpoints, eliminating discontinuities that can give rise to leakage errors. Different windowing functions can be used, such as Blackman, Hanning, or Hamming windowing functions, each with its own particular characteristics. Windowing functions tend to diminish leakage errors distant from the peaks in a power spectrum, but also tend to create wider peaks. Thus, they have the effect of redistributing rather than completely eliminating leakage. Also, because windowing functions actually change the data on which a DFT is performed, they tend to slightly distort frequency spectra.
Yet another technique is to xe2x80x9cresamplexe2x80x9d the waveform data at a sampling rate that is coherent with the frequencies of the signal being sampled. Resampling works by interpolating between actual points sampled at one rate to mathematically construct a series of points that appear to have been sampled at a different rate. Although resampling can be extremely effective for reducing leakage, it is computationally intensive and its accuracy can suffer from interpolation errors.
Still another technique for reducing leakage is to vary the rate of the sampling clock so that it precisely equals an integer multiple of every frequency found in the sampled signal. This technique is extremely effective, but requires expensive hardware. This approach is particularly expensive when a tester includes a large number of sample clocks, as is often the case.
Manufacturers of automatic test equipment (ATE or xe2x80x9ctestersxe2x80x9d) commonly seek to improve their products by providing less costly solutions to conventional testing problems. Great benefits can be gleaned by increasing tester performance while decreasing tester cost. To this end, there is a strong need to provide an inexpensive technique for reducing leakage in the spectra of signals sampled by automatic test systems.
With the foregoing background in mind, it is an object of the invention to reduce leakage in sampled signals without requiring a significant increase in tester cost.
To achieve the foregoing object, as well as other objectives and advantages, a technique for analyzing the frequency content of a sampled waveform includes assembling a list of N frequencies expected to be found in the sampled waveform. The sampled waveform is assumed to conform to a waveform model that mathematically corresponds to a sum of N sinusoids. Each of the N sinusoids has unknown amplitude and phase, and a frequency that equals a different one of the N frequencies in the list of frequencies. The technique solves for the unknown amplitudes and/or phases that best fit the model to the sampled data.
According to one illustrative embodiment, the technique described above is also used when the frequencies of a sampled waveform are not known in advance. According to this variation, a Fourier Transform is computed on a sampled waveform to produce a rough power spectrum. Peaks in the rough power spectrum are identified, and their frequencies are compiled to form the list of N frequencies. Other factors may be considered in compiling the list of N frequencies, for example, known stimuli to a device from which the sampled data is acquired, and other attendant circumstances. The technique described above is then conducted on the resulting list of N frequencies, to determine the precise amplitudes and/or phases of each of the N sinusoids.